Physica B 373 (2006) 240–244 Pseudogap phenomenon and superconductivity in a magnetic field Angsula Ghosh à Departamento de Fı´sica, UFAM, 3000-Japiim 69077-000, Manaus, AM, Brazil Received 16 November 2005; accepted 17 November 2005 Abstract We study the effect of a magnetic field on the d-density wave (DDW) in the presence of d x 2 y 2 superconducting order parameter (DSC) for high-temperature cuprates using a mean-field calculation of the tight binding model. The phase diagrams for the order parameter with doping are discussed. The phase diagram of the field with filling and also the dependence of the critical field (H c ) on the critical temperature (T c ) have been considered. The temperature dependence of the specific heat is also demonstrated. The effect of the field on the DDW order parameter and the superconducting gap are not alike. While the field suppresses the DSC gap, it tends to increase the DDW gap at the same doping. Moreover the gap to T c ratio increases with the field. The critical field has a power law dependence (H c –T 2 c ). r 2005 Elsevier B.V. All rights reserved. PACS: 71.10.Fd; 74.72.h; 71.27.+a; 71.10.Pm Keywords: High T c compounds; Magnetic field; Pseudogap The formation of the pseudogap below a characteristic temperature, T  is, by now, a well-established concept where the density-of-states is depleted in the underdoped phase of the high-T c cuprates. Various experiments, such as photoemission [1], specific heat [2], tunneling [3] and optical conductivity [4] have observed the pseudogap in cuprates. However, the origin of the pseudogap remains controversial and has been ascribed to two different scenarios, occurrence of a competing order parameter or to the presence of the precursor superconductivity. The magnetic effects are good candidates for distinguishing between the two scenarios. The pseudogap in the high- temperature superconductors has recently been considered as a d-density wave order (DDW) [5,6] where the particle hole pair of the same orientation form the condensate. The phase diagram of the cuprates are in agreement with this recent picture. Moreover, the experimental situation is now quite promising. The elastic neutron scattering [7] and various other experiments [8] are consistent with the above picture. The pseudogap exhibits a d x 2 y 2 -wave symmetry alike the superconducting gap below T c . However, the broken symmetry of the DDW state makes it different from the d x 2 y 2 -wave superconducting gap of the Cooper pairs. The magnetic field applied perpendicular to the CuO 2 planes has been a very efficient instrument to understand both the normal and superconducting phases of the cuprates. The magnetic field study of the superconductors in presence of the spin-density wave (SDW) has shown that the SDW order grows with magnetic field wheras the superconductivity is suppressed [9,10]. Most importantly, the field dependence of the SDW Bragg peak intensity has a cusp at the zero field. There are quite a few experiments that shed light on the effect of the magnetic field on the pseudogap. Nuclear magnetic resonance experiments on underdoped YBa 2 Cu 4 O 8 [11] exhibit a weak dependence of the pseudogap on an applied perpendicular magnetic field. Experiments on nearly optimally doped YBa 2 Cu 3 O 7d [12] share the same view. Moreover, a systematic determination of the pseudogap closing field has been made applying magnetic fields up to 60 T [13]. The above field and the temperature T  are related through the simple Zeeman-like expression that suggests the coupling of the magnetic field to the pseudogap by the Zeeman energy of the spin degrees ARTICLE IN PRESS www.elsevier.com/locate/physb 0921-4526/$ - see front matter r 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.physb.2005.11.150 à Tel.: +55 92 36474131; fax: +55 92 36474132. E-mail addresses: angsula@ufam.edu.br, angsula@if.usp.br.